Now if you're trying to get the most out of the items your retainer brings back you would want to deck them out in level appropriate HQ gear... but do you really need to?
I sent out my two retainers yesterday, a botanist in full hq gathering gear, and an arcanist dressed up like a snowman.
Both returned with an HQ item set and the same amount of experience. It's hard to say since it's just the first run but it seems that how "well" they're equiped doesn't immediately effect how much they level, but just the quality of the items they get since SE did mention that much.
The only risk I'm worried about is if SE programed in a failure scenario where if your retainer is underequiped they can't complete their mission... but I don't know if I'm over thinking that much.